U.S. patent number 6,087,981 [Application Number 09/147,851] was granted by the patent office on 2000-07-11 for method for pulse compression with a stepped frequency waveform.
This patent grant is currently assigned to Thomson-CSF. Invention is credited to Rodolphe Cottron, Eric Normant.
United States Patent |
6,087,981 |
Normant , et al. |
July 11, 2000 |
Method for pulse compression with a stepped frequency waveform
Abstract
The present invention relates to radars and sonars, and more
particularly to a synthetic-band technique of pulse compression
making it possible to reach a very high distance resolution.
Synthetic band consists in transmitting a waveform pattern
consisting of a string of N coherent elementary pulses, linearly
frequency-modulated, following one another at a recurrence
frequency F.sub.r, of rectangular frequency spectra of elementary
band B and of stepped carrier frequencies such that their frequency
spectra will link up exactly one ahead of another to form a global
spectrum of width N.times.B. On reception, the frequency spectra of
the signals received in return for the N elementary pulses of a
pattern are extracted by calculation, translated and juxtaposed so
as to reconstruct a global frequency spectrum of width N.times.B
and then compressed. Pulse compression is thus obtained which is
equivalent to that which would result from the transmission of a
waveform having a single pulse of frequency band N.times.B as
pattern, whereas only elementary pulses of frequency band of width
B were transmitted.
Inventors: |
Normant; Eric (Montigny le
Bretonneux, FR), Cottron; Rodolphe (Issy les
Moulineaux, FR) |
Assignee: |
Thomson-CSF (Paris,
FR)
|
Family
ID: |
9509472 |
Appl.
No.: |
09/147,851 |
Filed: |
March 22, 1999 |
PCT
Filed: |
July 21, 1998 |
PCT No.: |
PCT/FR98/01607 |
371
Date: |
March 22, 1999 |
102(e)
Date: |
March 22, 1999 |
PCT
Pub. No.: |
WO99/05543 |
PCT
Pub. Date: |
February 04, 1999 |
Foreign Application Priority Data
|
|
|
|
|
Jul 22, 1997 [FR] |
|
|
97 09285 |
|
Current U.S.
Class: |
342/134; 342/131;
342/132; 342/135; 342/192; 342/196; 342/202; 342/25D; 367/102;
367/118 |
Current CPC
Class: |
G01S
13/282 (20130101) |
Current International
Class: |
G01S
13/00 (20060101); G01S 13/28 (20060101); G01S
013/28 (); G01S 013/90 (); G01S 007/292 (); G01S
015/08 () |
Field of
Search: |
;342/118,130,131,132,134,135,192,195,196,201,202,203,204,25
;367/88,99,102,118,128 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Sotomayor; John B.
Attorney, Agent or Firm: Oblon, Spivak, McClelland, Maier
& Neustadt, P.C.
Claims
We claim:
1. Very high distance resolution pulse compression process for
radar or sonar characterized in that it consists:
in using on transmission a synthetic-band repetitive waveform
pattern consisting of a string of N linearly frequency-modulated
coherent elementary pulses following one another at a recurrence
frequency F.sub.r, of rectangular frequency spectra of elementary
band B and of stepped carrier frequencies such that their frequency
spectra will link up exactly one ahead of another to form a global
frequency spectrum of width N.times.B, the said N elementary pulses
following one another in any order corresponding via a permutation
p(k) to the natural order based on increasing carrier
frequencies;
in demodulating at reception the signal received in return for each
elementary pulse by the carrier frequency of the relevant
elementary pulse so as to extract the complex envelope
therefrom;
in filtering the signals received and demodulated by a filter which
passes the frequency band B of an elementary pulse;
in sampling the signals received, demodulated and filtered at a
sampling frequency of the order of the band B of the elementary
pulses, according to two time scales: one short-term scale, with
variable .tau. measuring the time which elapses between two
successive pulses of a pattern of the transmission waveform and
catering for a tagging of targets along a distance axis, the other
a longer-term scale with variable t, measuring the succession of
patterns of the transmission waveform and catering for a tagging of
targets along a Doppler or azimuth axis parallel to the direction
of movement of the radar or of the sonar with respect to the
targets;
in translating the frequency spectrum of the signal received in
return for a Kth pulse so as to set it back in its place within the
frequency spectrum of the global pattern of the transmitted
waveform by multiplying the samples of the return signal for a kth
elementary pulse by a complex exponential dependent on the time
variable T along the distance axis:
.tau..sub.0 being the lag after which storage of the digital
samples on the distance axis begins, .DELTA.f.sub.p(k) being the
carrier frequency gap of the kth elementary pulse with respect to
the central carrier frequency f.sub.c of the pattern;
in performing a distancewise spectral analysis of an oversampling,
in a ratio N, of the frequency-translated complex samples so as to
go, distancewise, from the time domain with variable .tau. to a
frequency domain with variable F and obtain a sampled frequency
spectrum for the return signal of each elementary pulse;
in selecting from the distancewise frequency spectrum obtained for
the signal received in return for a kth elementary pulse, the
samples belonging to a span centred around .DELTA.f.sub.p(k) with a
width equal to that of the band B of an elementary pulse;
in constructing, from the samples of the selected spans of the
distancewise frequency spectra of the signals in return for the
elementary pulses, a sampling of the product of the global
distancewise frequency spectrum of the signal received in return
for the set of elementary pulses of a synthetic-band waveform
pattern, times the conjugate of the global frequency spectrum of
the elementary pulses of a synthetic-band waveform pattern so as to
carry out filtering matched globally to the synthetic-band
waveform, and
in performing a distancewise inverse spectral analysis so as to
return to the distancewise time domain and obtain a
distance-compressed received signal.
2. Process according to claim 1, characterized in that the
distancewise spectral analysis of an oversampling, in a ratio N, of
the frequency-translated samples of the signal received in return
for an elementary pulse of order k consists:
in oversampling, in a ratio N, the frequency-translated complex
samples of the raw video signal received in return for an
elementary pulse of rank k, by inserting N-1 null samples between
each of them, and
in performing a distancewise discrete Fourier transform on the
oversamples obtained so as to go, distancewise, from the time
domain with variable .tau. to a frequency domain with variable
F.
3. Process according to claim 1, characterized in that the
distancewise spectral analysis of an oversampling, in a ratio N, of
the frequency-translated samples of the signal received in return
for an elementary pulse of order k consists:
in performing a distancewise discrete Fourier transform on the
frequency-translated complex samples so as to go distancewise from
the time domain with variable .tau. to a frequency domain with
variable F, and
in duplicating N times the sampled frequency spectrum obtained.
4. Process according to claim 1, characterized in that the
construction of the sampling of the product of the global frequency
spectrum of the signal received times the conjugate of the global
frequency spectrum of a synthetic-band waveform pattern
consists:
in multiplying the samples of the selected span of the distancewise
frequency spectrum of the signal received in return for a kth
elementary pulse by the conjugate X.sub.1,k *(F) of the frequency
spectrum of this kth transmitted elementary pulse, so as to carry
out a matched filtering, X.sub.1,k (.function.) complying with the
relation:
where P(F) is the spectrum of an elementary pulse transmitted at
the central carrier frequency of the synthetic-band waveform
pattern, and
in juxtaposing the frequency spectrum spans obtained for the
signals received in return for the elementary pulses after matched
filterings, so as to produce a global frequency spectrum which
would correspond to that of a signal obtained in response to a
linearly frequency-modulated single pulse of band N.times.B, after
matched filtering.
5. Process according to claim 1, characterized in that the
construction of the sampling of the product of the global frequency
spectrum of the signal received times the conjugate of the global
frequency spectrum of a synthetic-band waveform pattern
consists:
in multiplying the samples of the selected span of the distancewise
frequency spectrum of the signal received in return for a kth
elementary pulse by the conjugate X.sub.1,k.sup.(s)* (.function.)
of the frequency spectrum of this kth transmitted elementary pulse,
so as to carry out a matched filtering, X.sub.1,k.sup.(s)
(.function.) complying with the relation:
where P(F) is the spectrum of an elementary pulse transmitted at
the central carrier frequency of the synthetic-band waveform
pattern and .function..sub.dc a mean Doppler parmeter conveying the
influence of the azimuthal time variable t on the radar/target
outward/return propagation time, and
in juxtaposing the frequency spectrum spans obtained for the
signals received in return for the elementary pulses after matched
filterings, so as to produce a global frequency spectrum which
would correspond to that of a signal obtained in response to a
linearly frequency-modulated single pulse of band N.times.B, after
matched filtering.
6. Process according to claim 1, characterized in that the
construction of the sampling of the product of the global frequency
spectrum of the signal received times the conjugate of the global
frequency spectrum of a synthetic-band waveform pattern
consists:
in juxtaposing the samples of the selected spans of the frequency
spectra of the signals received in return for the elementary
pulses, and
in multiplying the samples of the global frequency spectrum
obtained by the conjugate X.sub.1 *(F) of the global frequency
spectrum resulting from the juxtaposition of the frequency spectra
of the elementary pulses transmitted, X.sub.1 (F) complying with
the relation: ##EQU48## where P(F) is the spectrum of an elementary
pulse transmitted at the central carrier frequency of the
synthetic-band waveform pattern.
7. Process according to claim 1, characterized in that the
construction of the sampling of the product of the global frequency
spectrum of the signal received times the conjugate of the global
frequency spectrum of a synthetic-band waveform pattern
consists:
in juxtaposing the samples of the selected spans of the frequency
spectra of the signals received in return for the elementary
pulses, and
in multiplying the samples of the global frequency spectrum
obtained by the conjugate X.sub.1.sup.(s)* (F) of the global
frequency spectrum resulting from the juxtaposition of the
frequency spectra of the elementary pulses transmitted,
X.sub.1.sup.(s) (F) complying with the relation: ##EQU49## where
P(F) is the spectrum of an elementary pulse transmitted at the
central carrier frequency of the synthetic-band waveform pattern
and .function..sub.dc a mean Doppler parmeter conveying the
influence of the azimuthal time variable t on the radar/target
outward/return propagation time.
8. Process according to claim 1, characterized in that it
furthermore consists in carrying out a complementary initialization
processing in respect of Doppler processing on the samples of the
distance-compressed signal received, arrayed as a two-dimensional
table v.sub.2 (.tau., t) as a function of the two time variables
.tau. along the distance axis and t along the azimuth axis, the
said complementary processing consisting, after having performed in
succession a distancewise Fourier transform and then an azimuthal
Fourier transform on the signal so as to go into the distancewise
frequency domain with a frequency variable F and azimuthal
frequency domain with a frequency variable f and obtain a table of
samples V.sub.2 (F,f), in multiplying the sequences of samples
belonging to the various distance spectral regions of the
elementary pulses splitting into N sub-bands of width B, the band
N.times.B of the frequency variable F, by a phase corrective term
such that:
where .DELTA.t.sub.k is the lag separating the kth relevant pulse
from the middle of the pattern of the transmission waveform of
which it forms part and .function..sub.dc a mean Doppler parameter
conveying the influence of the time variable t on the radar/target
outward/return propagation time.
Description
BACKGROUND OF THE INVENTION
The present invention relates to radars and sonars. It is known
practice to improve the distance resolution of a radar or a sonar
by the technique of pulse compression. Indeed, the distance
resolving power .DELTA.D of a radar or a sonar is related to the
duration .tau. at reception of the pulse waveform transmitted by
the relation: ##EQU1## where c is the wave propagation speed. Since
the duration .tau. and the width of the frequency spectrum or
passband .DELTA.F of the pulse waveform transmitted are related by
a relation of the form:
it is also possible to state that the distance resolving power of a
radar or a sonar is inversely proportional to the passband of its
pulse waveform.
The technique of pulse compression consists in lengthening the
pulse waveform on transmission and then in compressing it on
reception, thereby limiting the peak power to be transmitted. To
put it into practice, use is generally made, at transmission, of a
linearly frequency-modulated quasi-rectangular pulse and at
reception, of a compression filter which delays the various
frequency components of the pulse differently so as to make them
coincide. The degree of compression and hence the distance
resolving power is limited by the capacity available for producing
large-band frequency-modulated pulses.
One way of countering this limitation consists in employing a
particular waveform known by the designation: "synthetic band"
(otherwise known as Stepped Frequency) and described in particular
in the book by J. P. Hardange, P. Lacomme, J. C. Marchais,
entitled: "Radars aeroportes et spatiaux" [Airborne and space
radars], published by Masson 1995, pages 165-167.
Synthetic band consists in transmitting a waveform composed of a
repetitive pattern of N successive pulses of duration T, of
passband B, spaced apart by an interval .DELTA.T in time and
.DELTA.F in frequency, the first being centred on f.sub.0, the
second on f.sub.0 +.DELTA.f, the third on f.sub.0 +2.DELTA.f,
etc.
After demodulation by its carrier frequency, each pulse received is
filtered by a matched filter and then sampled and converted into
digital. The processing continues with a discrete Fourier transform
on N samples belonging to the same distance gate and acquired in
succession for the N transmission frequencies of the N pulses of
the waveform transmitted.
The response .vertline.c(.DELTA.t).vertline. of the receiver
matched to the waveform, to the echo returned by a target after a
time t.sub.0, which results from the discrete Fourier transform,
corresponds to that of the filter matched to each elementary pulse
multiplied by a function similar to a sinc: ##EQU2## It has a 3 dB
width of: ##EQU3## and contains a periodic term of period
1/.DELTA.f.
The resolution is fixed by the width 1/N.DELTA.f of the reception
spectrum of the pattern of the waveform transmitted whereas it
would be only 1/B for a transmission waveform pattern limited to an
elementary pulse.
To comply with the sampling theorem, the sampling period
.tau..sub.e must be less than the inverse 1/B of the band of the
elementary pulses of the waveform. Moreover, to avoid distance
ambiguities, the analysis performed by the Fourier transform must
cover at least the m distance gates over which the response of a
target to a pulse at the output of the matched filter extends, this
being conveyed with regard to the elementary gap .DELTA.f between
the carrier frequencies of the pulses, the sampling period
.tau..sub.e and the passband B of each pulse by the condition:
##EQU4## This condition imposes some overlap between the frequency
spectra of the elementary pulses which implies that the distance
resolution is improved by only a factor N.DELTA.f/B which is less
than N.
Another counterargument to the use of N successive pulses in the
pattern of the waveform transmitted is that the coverage of a given
swathe, with a certain resolution, takes N times as long as for a
conventional pulse compression radar. If the constraint is to
comply with a minimum recurrence frequency as in the case of a
mapping radar, the dimension of the swathe is reduced in a ratio
N.
SUMMARY OF THE INVENTION
The purpose of the present invention is to obtain a very high
distance resolution from a transmitted waveform pattern consisting
of a string of N elementary pulses of average resolution, of
rectangular frequency spectra of band B and of carrier frequencies
stepped in such a way that their frequency spectra will link up
exactly to form an equivalent spectrum of width N.times.B.
It aims to recreate at reception a response to an equivalent pulse
of frequency band N.times.B equal to that of the synthetic-band
waveform pattern and, consequently, to improve the resolution by a
factor N, doing so without the appearance of additional ambiguities
as in the known synthetic-band process.
The advantages of transmitting a waveform pattern with a synthetic
band relative to that of some other hypothetical waveform pattern
having a frequency band N.times.B over a single elementary pulse
are:
a smaller signal sampling frequency at reception required to obtain
a given resolution (decrease by a factor N);
a greater capacity to resist the saturating of the receiver by
intentional or unintentional electromagnetic jamming since the
passband of the receiver is N times smaller;
a greater resistance to the dispersivity of the antenna during
electronic scanning of the beam.
On the other hand, it retains the drawback of the known
synthetic-band process, namely of reducing the dimension of the
swathe by a factor N.
The subject of the invention is a very high distance resolution
pulse compression process for radar or sonar consisting:
in using on transmission a synthetic-band repetitive waveform
pattern consisting of a string of N linearly frequency-modulated
coherent elementary pulses following one another at a recurrence
frequency F.sub.r, of rectangular frequency spectra of elementary
band B and of stepped carrier frequencies such that their frequency
spectra will link up exactly one ahead of another to form a global
frequency spectrum of width N.times.B, the said N elementary pulses
following one another in any order corresponding via a permutation
p(k) to the natural order based on increasing carrier
frequencies;
in demodulating at reception the signal received in return for each
elementary pulse by the carrier frequency of the relevant
elementary pulse so as to extract the complex envelope
therefrom;
in filtering the signals received and demodulated by a filter which
passes the frequency band B of an elementary pulse;
in sampling the signals received, demodulated and filtered at a
sampling frequency of the order of the band B of the elementary
pulses, according to two time scales: one short-term scale, with
variable .tau. measuring the time which elapses between two
successive pulses of a pattern of the transmission waveform and
catering for a tagging of targets along a distance axis, the other
a longer-term scale with variable t, measuring the succession of
patterns of the transmission waveform and catering for a tagging of
targets along a Doppler or azimuth axis parallel to the direction
of movement of the radar or of the sonar with respect to the
targets;
in translating the frequency spectrum of the signal received in
return for a Kth pulse so as to set it back in its place within the
frequency spectrum of the global pattern of the transmitted
waveform by multiplying the samples of the return signal for a kth
elementary pulse by a complex exponential dependent on the time
variable .tau. along the distance axis:
.tau..sub.0 being the lag after which storage of the digital
samples on the distance axis begins, .DELTA.f.sub.p (k) being the
carrier frequency gap of the kth elementary pulse with respect to
the central carrier frequency f.sub.c of the pattern;
in performing a distancewise spectral analysis of an oversampling,
in a ratio N, of the frequency-translated complex samples so as to
go, distancewise, from the time domain with variable .DELTA. to a
frequency domain with variable F and obtain a sampled frequency
spectrum for the return signal of each elementary pulse;
in selecting from the distancewise frequency spectrum obtained for
the signal received in return for a kth elementary pulse, the
samples belonging to a span centred around .DELTA.f.sub.p (k) with
a width equal to that of the band B of an elementary pulse;
in constructing, from the samples of the selected spans of the
distancewise frequency spectra of the signals in return for the
elementary pulses, a sampling of the product of the global
distancewise frequency spectrum of the signal received in return
for the set of elementary pulses of a synthetic-band waveform
pattern, times the conjugate of the global frequency spectrum of
the elementary pulses of a synthetic-band waveform pattern so as to
carry out filtering matched globally to the synthetic-band
waveform, and
in performing a distancewise inverse spectral analysis so as to
return to the distancewise time domain and obtain a
distance-compressed received signal.
The distancewise spectral analysis of an oversampling, in a ratio
N, of the frequency-translated samples of the signal received in
return for an elementary pulse of order k may be carried out:
by oversampling, in a ratio N, the frequency-translated complex
samples, by inserting N-1 null samples between each of them,
and
by performing a distancewise discrete Fourier transform on the
oversamples obtained so as to go, distancewise, from the time
domain with variable .tau. to a frequency domain with variable
F.
The distancewise spectral analysis of an oversampling, in a ratio
N, of the frequency-translated samples of the signal received in
return for an elementary pulse of order k can also be carried
out:
by performing a distancewise discrete Fourier transform on the
frequency-translated complex samples so as to go distancewise from
the time domain with variable .tau. to a frequency domain with
variable F, and
by duplicating N times the sampled frequency spectrum obtained.
This latter way of carrying out the distancewise spectral analysis
of an oversampling, in a ratio N, of the frequency-translated
complex samples of the signal received in response to the
transmission of an elementary pulse has a definite advantage over
the previous one since it makes it possible to replace the
calculation of N Fourier transforms of large size with that of N
Fourier transforms of smaller size, the size ratio being of the
order of N.
The construction of the sampling of the product of the global
frequency spectrum of the signal received times the conjugate of
the global frequency spectrum of a synthetic-band waveform pattern
can be carried out:
by multiplying the samples of the selected span of the distancewise
frequency spectrum of the signal received in return for a kth
elementary pulse by the conjugate X.sub.1,k *(F) of the frequency
spectrum of this kth transmitted elementary pulse, so as to carry
out a matched filtering, X.sub.1,k (.function.) complying with the
relation:
or, more accurately, with the relation:
P(F) being the spectrum of an elementary pulse transmitted at the
central carrier frequency of the synthetic-band waveform pattern
and .function..sub.dc a mean Doppler parameter conveying the
influence of the time variable t on the radar/target outward/return
propagation time, and
by juxtaposing the spans of the frequency spectra obtained, after
matched filterings, for the signals received in return for the
elementary pulses, so as to produce a global frequency spectrum
which would correspond, after matched filterings, to that of a
signal obtained in response to a linearly frequency-modulated
single pulse of band N.times.B.
The construction of the sampling of the product of the global
frequency spectrum of the signal received times the conjugate of
the global frequency spectrum of a synthetic-band waveform pattern
can likewise be carried out:
by juxtaposing the samples of the selected spans of the frequency
spectra of the signals received in return for the elementary
pulses, and
by multiplying the samples of the global frequency spectrum
obtained by the conjugate X.sub.1 *(F) of the global frequency
spectrum resulting from the juxtaposition of the frequency spectra
of the elementary pulses transmitted, X.sub.1 (F) complying with
the relation: ##EQU5## or, more accurately, with the relation:
##EQU6## P(F) being the spectrum of an elementary pulse transmitted
at the central carrier frequency of the synthetic-band waveform
pattern and .function..sub.dc a mean Doppler parameter conveying
the influence of the time variable t on the radar/target
outward/return propagation time.
Advantageously, when the reception signal is intended to undergo
Doppler processings, whether these be spectral analyses peculiar to
Doppler-pulse radars or mapping radar SAR processing, the above
process for very high distance resolution pulse compression is
supplemented with a complementary processing for initializing the
Doppler processings. This complementary processing is effected on
the received-signal samples arrayed as a two-dimensional table
v.sub.2 (.tau., t), as a function of the two time variables: .tau.
along the distance axis and t along the Doppler axis. It consists,
after having performed in succession a distancewise Fourier
transform and then an azimuthal Fourier transform on the signal so
as to go into the distancewise frequency domain with the frequency
variable F and azimuthal frequency domain with the frequency
variable f and obtain a table of samples V.sub.2 (F,f), in
multiplying the sequences of samples belonging to the various
distance spectral regions of the elementary pulses splitting into N
sub-bands of width B, the band N.times.B of the frequency variable
F, by a phase corrective term such that:
where .DELTA.t.sub.k is the lag separating the kth relevant pulse
from the middle of the pattern of the transmission waveform of
which it forms part and .function..sub.dc a mean Doppler parameter
conveying the influence of the time variable t on the radar/target
outward/return propagation time.
This corrective term b.sub.r.sup.k (.function.) compensates for a
phase shift term dependent on the rank of the elementary pulses,
introduced by chopping the pattern of the transmission signal into
several elementary pulses of stepped carriers.
The use of a repetitive waveform pattern consisting of a string of
N coherent elementary pulses of stepped carrier frequencies which
do not follow one another in a natural order of increasing or
decreasing carrier frequencies but according to a certain
permutation with respect to such a natural order, makes it possible
to reduce the distance ambiguity in so far as this makes it
possible to adopt a gap between the carrier frequencies of two
successive pulses in a pattern which is larger than the unit step
and which increases the rejection power of the band filter of the
receiver in regard to the ambiguous responses which do not
correspond to the last pulse transmitted but to a previous
pulse.
BRIEF DESCRIPTION OF THE DRAWINGS
Other characteristics and advantages of the invention will emerge
from the description below of an embodiment given by way of
example. This description will be given in conjunction with the
drawing, in which:
a FIG. 1 represents a timing diagram for the synthetic-band
transmission waveform pattern used in the very high distance
resolution pulse compression process according to the
invention;
a FIG. 2 represents a schematic diagram of a radar implementing the
transmission waveform pattern illustrated in FIG. 1;
a FIG. 3 represents a schematic diagram of a distance pulse
compression processing according to the invention;
FIGS. 4 and 5 detail two ways of carrying out a spectral analysis
of the oversampled signal which can be used in the course of a
pulse compression processing according to the invention;
FIGS. 6 and 7 detail two ways of reconstructing the global
frequency spectrum of the reception signal in response to the
transmission of a synthetic-band waveform pattern and of
compressing this global frequency spectrum, which can be used in
the course of a pulse compression processing according to the
invention; and
a FIG. 8 represents a schematic diagram of a Doppler initialization
preprocessing advantageously supplementing a pulse compression
processing according to the invention in the case of a subsequent
implementation of a Doppler processing.
As shown in FIG. 1, the transmission waveform which it is proposed
to use consists of the repetition, at a recurrence frequency
F'.sub.r +1/T'.sub.r, of a pattern consisting of N elementary
pulses of like duration T repeated at a recurrence frequency
F.sub.r =1/T.sub.r. Without loss of generality, it will be assumed
in what follows that:
Under the assumption that the elementary pulses are linearly
frequency-modulated according to the same slope .alpha., the
expression for their complex envelope is given by the relation:
##EQU7##
The frequency band B occupied by an elementary pulse is equal
to:
Assuming that the product B.times.T is sufficiently large
(>200), and applying the stationary phase principle, the
frequency spectrum of this elementary waveform is given by:
##EQU8## This frequency spectrum has a quasi-rectangular
envelope.
In what follows we shall restrict ourselves to elementary pulses of
this type although this is not in the least necessary in theory,
since it is by far the most widespread in operational radar imaging
systems. Furthermore, the fact that the frequency spectrum of
pulses of this type is quasi-rectangular makes it a candidate
particularly suited to the compression process to be described.
Each elementary pulse in the waveform pattern will be distinguished
by its rank k referenced with respect to the middle of the pattern.
For an odd number of elementary pulses N, the rank k lies between:
##EQU9## For an even number of elementary pulses N, the rank k lies
between: ##EQU10##
The information useful for obtaining the resolution on the distance
axis is here distributed over a series of N pulses rather than
being contained in a single pulse as is the case for conventional
radar imaging systems employing a repetitive transmission waveform
pattern consisting of a series of identical pulses. Each pulse of
the series has a relative lead or delay with respect to another. In
the following description, we have chosen to calculate this lead or
this delay with respect to a reference situated in the middle of
the pattern. This makes it possible in radar imaging applications
using synthetic aperture radar SAR to provide a symmetric Doppler
phase history.
Under these conditions, the time swift of each pulse as a function
of its
rank is given by: ##EQU11##
Let B be the useful band associated with each elementary pulse,
then the N carrier frequencies used to modulate the elementary
pulses are contrived in such a way as to be spaced B apart. This
makes it possible to reconstruct, over the synthetic band, an
equivalent global spectrum with no void. Thus, each elementary
pulse is modulated on a carrier frequency, f.sub.k, which depends
on the rank of the pulse in the pattern. If in a pattern the pulses
are ranked in order of increasing carrier frequency, the expression
for the carrier frequency f.sub.k of the pulse of rank k is given
by:
where f.sub.c, denotes the central carrier frequency of the
pattern.
However, to reduce the level of distance ambiguity, it is
beneficial to transmit the pulses making up a pattern in an order
which differs from the natural order of increasing or decreasing
carrier frequencies. This is because, so as to ease the filtering
carried out by the bandpass reception filter, it is beneficial to
arrange matters in such a way that the pulses follow one another in
a pattern with carrier frequency gaps of greater than the unit
step. A pulse of rank k in the pattern then has a carrier frequency
f.sub.p(k) which is not the frequency f.sub.k but another
frequency, f.sub.k', the index k' corresponding to the index k via
a permutation p. Stated otherwise, the spectral region occupied by
a pulse of rank k is given by: ##EQU12##
FIG. 2 gives an example of a schematic diagram of a radar
implementing this waveform. Depicted therein is an antenna 10
linked by a circulator 11 to a transmission part and to a reception
part.
The transmission part comprises a waveform generator GFO 12 which
produces, at an intermediate carrier frequency f.sub.Fi, an
elementary pulse with linear frequency modulation. This waveform
generator GFO 12 is linked to the antenna 10 by way of the
circulator 11 and of a mixer 13 which receives from a source of
frequencies SF 14, various carrier frequencies which make it
possible to arrange matters such that the N elementary pulses of
the waveform applied to the antenna 10 each modulate the
frequencies f.sub.1, . . . , f.sub.k, . . . , f.sub.N.
The reception part comprises, at the output of the circulator 11, a
mixer 15 which mixes the signal received by the antenna 10 with the
carrier frequencies emanating from the source of frequencies SF 14
so as to refer the return echoes from the elementary pulses of the
transmitted waveform to an intermediate frequency f.sub.Fi. This
mixer 15 is followed by a bandpass filter 16 matched to the
frequency band of an elementary pulse and by an amplitude/phase
demodulator associated with an analog/digital converter DAP/CAN 17
which provides a sampling of the complex envelope of the signal
received and demodulated.
To allow pulse compression at reception of the transmitted waveform
pattern, it is necessary to ensure coherence between the various
elementary pulses of which it consists. This requires the source of
frequencies SF 14 to be coherent for each of the N carrier
frequencies generated. Moreover, for certain applications, it can
happen that the useful return corresponding to a pulse of rank k
occurs in the reception window for a pulse of different rank. This
then necessitates either N different coherent sources of frequency
associated with each of the carrier frequencies, or a single source
of frequencies which is capable of keeping the phase reference
associated with. a given carrier after having transmitted on
several other frequencies in the meantime.
It is noted that by virtue of the filtering matched to the
elementary pulse, the number of distance ambiguities does not
increase for the relevant waveform as compared with a waveform
consisting of the same elementary pulse repeated at the recurrence
frequency F.sub.r. This is due to the fact that the returns
corresponding to different ranks of the elementary pulse in respect
of which the frequency source is adjusted at the time are rejected
by the bandpass reception filter.
In all generality, the echo signal v.sub.o,k (.tau., t) in response
to the transmitted pulses of kth rank can be regarded as the result
of a correlation in two dimensions .tau. and t between the complex
backscattering coefficient .gamma..sub.k (.tau., t) of the targets
with coordinates .tau. and t for the carrier frequency of the
pulses of rank k, and the product of the waveform p() of an
elementary pulse of rank k transmitted times an impulse response
h.sub.az,k (). The waveform p() of the relevant elementary pulse of
rank k is delayed by the time required for the outward/return
propagation thereof up to the desired point with coordinates .tau.
and t, the delay varying not only as a function of the distance
coordinate .tau. but also as a function of the azimuth coordinate t
so as to take account of the migration phenomenon occasioned by a
possible movement of the radar with respect to the targets. The
azimuthal impulse response h.sub.az,k () conveys a synthetic
antenna or SAR effect resulting from the azimuthal aperture width
of the antenna of the radar and of the possible movement of the
radar with respect to the targets.
By adopting for the waveform of an elementary pulse and the impulse
response of the synthetic antenna effect a common time origin,
along the azimuth coordinate t, independent of the order of a pulse
in a synthetic-band waveform pattern, it follows that:
##EQU13##
T being the duration of an elementary pulse,
.tau..sub.0 being the lag after transmission of an elementary
pulse, whereafter consideration of the receipt signal begins,
T.sub.e the time of illumination of a target,
.tau..sub.c being the variation in the radar/target outward/return
propagation time during the time of illumination T.sub.e,
.DELTA.t.sub.k the time shift of the pulse of rank k.
The azimuthal impulse response h.sub.az,k due to the synthetic
antenna effect, that is to say to the combined effect of an antenna
having a certain azimuthal aperture and of the azimuthal movement
of the radar with respect to the targets, is expressed, in a
well-known manner, by the relation: ##EQU14## where g.sub.az is the
azimuthal transmission/reception antenna diagram of the radar and
f.sub.p(k) the carrier frequency of the elementary pulse of rank
k:
f.sub.c being the central carrier frequency of a pattern and
.DELTA.f.sub.p(k) the gap of the carrier frequency of the kth pulse
with respect to the central carrier frequency of the pattern
f.sub.c, given that the elementary pulses are not in natural order
but permuted so as to improve the effectiveness of the bandpass
reception filter.
According to the expression for the echo signal v.sub.o,k (.tau.,
t) in response to the transmitted pulses of rank k, it is apparent
that there is great synergy with the case of the conventional
waveform consisting of a string of elementary pulses of like
carrier frequency. It is therefore conceivable to seek to extract
from the reception signal following the transmission of a
synthetic-band waveform with N elementary pulses of different
carrier frequencies, N conventional raw reception video signals
with parameters matched to each elementary pulse (.DELTA.t.sub.k,
Doppler parameters) and then to fuse these N independent raw video
signals by interposing the recurrences as a function of their rank
so as to try to approximate the echo signal received by a
conventional waveform consisting of one and the same pulse of band
N.times.B.
The guideline for the pulse compression processing in respect of a
synthetic-band waveform will then consist in synthesizing, from the
N raw reception video signals extracted from the signals received
in response to the N elementary pulses of the synthetic-band
waveform, a global spectrum of width N times greater than the
spectrum of an elementary pulse and then in compressing the signal
corresponding to this global spectrum.
The synthesis of a global spectrum of width N times greater than
the spectrum of an elementary pulse begins by setting each spectrum
of the N signals received in response to the N elementary pulses in
its place within the global spectrum of a synthetic-band waveform.
This placement is achieved by translating the spectrum of the
signal received in response to an elementary pulse of rank k by a
value .DELTA..function..sub.p(k), by multiplying the raw video
signal received in response to an elementary pulse of rank k
by:
After multiplication by the translation signal, a Fourier transform
is performed along the distance coordinate .tau. so as to extract
the frequency spectrum of the signal received in echo to a
transmitted pulse of rank k. This spectrum V.sub.1,k (.function.,
t) is expressed as a function of the signal value V.sub.0,k (.tau.,
t) taken in relation (1) by: ##EQU15##
Replacing the azimuthal impulse response to an elementary pulse of
rank k, h.sub.az,k () by its value taken in relation (2) and the
term .DELTA..function..sub.p(k) by its value taken in relation (3),
and performing the necessary simplifications, we obtain:
##EQU16##
It is then appreciated that, by virtue of the spectrum translation
operation, it is possible to express the spectrum of the raw video
signal received in response to a pulse of rank k on the basis of an
azimuthal impulse response which no longer depends on the carrier
frequency associated with the rank of the elementary pulse but only
on the central frequency fc of the pattern of the synthetic-band
waveform. The phase shift of the Doppler history is now determined
by the central carrier frequency of the pattern of the
synthetic-band waveform. However, the presence of a delay specific
to a waveform of rank k is observed, a topic to which we shall
return subsequently.
Another important point to be noted is the influence of the
knowledge of the instant To onwards of which storage of the digital
samples on the distance axis begins. This is because, contrary to
the conventional waveform, this term introduces by reason of the
change of carrier frequency a phase shift which depends on the rank
of the relevant elementary pulse. It is compensated for here in the
spectrum translation signal in which the absolute time
(.tau.+.tau..sub.0) has been considered. If this phase term with
the expression:
were not compensated for, there would be parasitic phase-shifts for
each sub-band over the entire synthetic band, and this would
considerably degrade the distancewise impulse response of a radar
imaging system.
In practice, the signal received takes the form of digital samples
with a sampling frequency F.sub.e matched to the passband of an
elementary pulse:
This sampling frequency is insufficient to reconstruct the
frequency spectrum of width N.times.B of a single pulse equivalent
to the N elementary pulses of the synthetic-band waveform. Several
solutions can be envisaged for arriving at the spectrum of a raw
video signal received in return for a pulse of order k, which is
oversampled and frequency-translated.
A first solution consists in:
oversampling, by a factor N, the raw video signal received in
response to each elementary pulse, by inserting (N-1) null samples
between each starting sample, so as to make the new sampling
frequency compatible with the N times greater width of the
synthetic band,
multiplying the oversampled raw video signal obtained by the
complex exponential spectrum translation signal:
calculating by DFT the distancewise Fourier transform of the result
along the distance coordinate .tau. and
retaining only the useful samples of the frequency spectrum, that
is to say of those belonging to the useful spectral region of the
elementary pulse processed.
To understand the influence of the oversampling operation on the
result of the discrete Fourier transform, we compare the results
obtained when oversampling is or is not carried out. Let:
in the absence of oversampling, (X.sub.k).sub.0.ltoreq.k<M be
the samples of the raw video reception signal and
(X.sub.k).sub.0.ltoreq.k<M those of the discrete Fourier
transform resulting therefrom and
in the presence of an oversampling of ratio N,
(y.sub.m).sub.0.ltoreq.m<NM be the oversamples of the raw video
reception signal and (y.sub.m).sub.0.ltoreq.m<NM those of the
discrete Fourier transform resulting therefrom.
By definition we have: ##EQU17## By making, in the expression for
Y, the change of variable j=kN+1, it follows that: ##EQU18## or
again, taking the null oversamples into account: ##EQU19##
It is then observed that the spectrum of the oversampled signal is
periodic and formed of a succession of N repetitions of the
spectrum of the starting signal.
This observation leads to an alternative solution, which is less
expensive computationally, for obtaining the spectrum of the
oversampled signal. To obtain the spectrum of the oversampled
signal it is in fact possible to exploit its periodicity so as to
calculate only one of its periods which corresponds to the discrete
Fourier transform of the starting signal, and then to complete. it
by repeating the calculated period.
This alternative solution is compatible with the initial desire to
translate the spectrum of the starting signal by a frequency
.DELTA.f.sub.p(k) which may be greater than the sampling frequency
F.sub.e.
Thus, if we apply the translation signal whose samples are defined
by: ##EQU20## the starting signal is merely translated by
.DELTA.f.sub.p(k) mod F.sub.e. However, given that the spectrum of
the oversampled signal has been reconstructed by juxtaposing N
periods, it follows that: ##EQU21## Since, moreover, the frequency
jump .DELTA.f.sub.p(k) is compatible with the new sampling
frequency Nf.sub.e, there exists an index j such that:
Thus, by duplicating the spectrum of the starting signal, we do
indeed obtain the spectrum of the signal oversampled at NF.sub.e
and translated by .DELTA.f.sub.p(k).
This alternative solution for obtaining the spectrum of the raw
video signal received in response to an elementary pulse of order
K, oversampled in a ratio N and frequency-translated by the gap
.DELTA.f.sub.p(k) exhibited by the carrier of this pulse of rank k
with respect to the central frequency of the pattern fc, which
consists, after having frequency-translated the raw video reception
signal, in calculating.the discrete Fourier transform thereof so as
to obtain the base period of the spectrum and in juxtaposing N of
these periods to obtain the complete spectrum, is very beneficial
from the point of view of the amount of computation demanded. This
is because, it makes it possible, to first order, to replace the
calculation of N FFTs of large size by N FFTs of smaller size, the
size ratio being of the order of N.
Once the elementary spectra of the raw video signals received in
response to the elementary pulses of the pattern of the
synthetic-band waveform have been obtained and realigned, the
global spectrum of the reception signal in response to the pattern
of the synthetic-band waveform is reconstructed by juxtaposing the
various elementary spectra. From the mathematical point of view,
this amounts to constructing a signal V.sub.1 (F, t) of the form:
##EQU22## where the presence of the rectangle function connotes
that, in each
elementary spectrum, the useful frequency bins are selected, the
others being rejected.
Once the global spectrum of the reception signal in response to the
synthetic-band waveform pattern is obtained, it is possible to
proceed with the pulse compression proper. The latter is achieved
by multiplying the samples of the global spectrum by those of the
spectrum of the matched filter. The case of the conventional
waveform provides the inspiration for building the samples of the
spectrum of the matched filter whilst complying with the specific
features of the synthetic band.
If no calibration signals are available, it is ossible, in order to
build the samples of the spectrum of the matched filter, to start
from the samples of the theoretical elementary pulse p(.tau.) and
then to subject this starting signal to exactly the same processing
as that just described for the signal received. That is to say,
this signal is duplicated N times so as to construct a complete
pattern. For each of the elementary pulses, the spectrum
translation and oversampling are performed in accordance with the
index thereof in the pattern. The following signals are thus
obtained:
Construction of the synthetic band for these reference signals
leads to: ##EQU23##
The expression for the transfer function Hi of the matched filter
is then given by:
To control the level of the side lobes of the impulse response of
the matched filter, a weighting window which is effective in the
case of the conventional waveform is introduced into the above
expression. This effective weighting can be written in the form:
##EQU24## where W(F) is the useful weighting window and G.sub.proc
is a constant factor compensating for the gain afforded by the
processing which is optional.
Thus, the complete expression for the transfer function of the
matched filter is given, in the general case, by: ##EQU25##
In order to take certain defects in the radar
transmission/reception chain into account, it is preferred to
transmit without exterior radiation of energy by the antenna,
receive and record a number of synthetic-band waveform patterns.
After averaging, a reference pattern with N elementary pulses is
available characterizing the behaviour of the radar
transmission/reception chain. The transfer function of the matched
filter is then built from the digital samples of these elementary
reference pulses in the same way as for the theoretical pattern. It
should however be remembered that the .tau..sub.0 individual to
these pulses must be taken into account in generating the frequency
translation signals. This is because the .tau..sub.0 of the
calibration signals is in general different from that of the
signals received during normal operation.
From the mathematical point of view, the signal V.sub.2 (F, t)
obtained after matched filtering in the distancewise frequency
domain and azimuthal time domain has the following expression:
##EQU26## it follows that: ##EQU27##
To return to the distancewise time domain, a distancewise inverse
Fourier transform is performed on the signal obtained. Having
finished this stage, access is available to the radar/target
distance information required to perform the operations for
correcting the parasitic motion of the carrier of the radar or for
taking into account the non-stationarities in the impulse response
of the radar system.
The signal V.sub.2 (.tau., t) obtained after the distancewise
inverse Fourier transform is expressed by: ##EQU28## the operator
*.sub..tau. denoting a convolution in the distance coordinate
.tau..
The latter expression shows that, in a manner similar to the
conventional waveform, the signal obtained is the result of
convolving the impulse response after distancewise processing and
the sought-after signal, itself convolved with the azimuthal
impulse response.
To compensate for the constant gain afforded by the processing, the
gain compensation factor G.sub.proc must be given the following
value: ##EQU29##
In practice, the distancewise inverse Fourier transform is
implemented in the form of a DFT.
By examining more carefully the expression for the signal obtained
V.sub.2 (.tau., t), it is observed that the novelty of the
synthetic-band waveform is to introduce a dependency on the
azimuthal impulse response with regard to the relevant distance
spectral region, doing so through the delays .DELTA.t.sub.k.
Returning to the expression of relation (4) detailing the azimuthal
impulse response, it may be seen that the azimuthal impulse
response introduces a parasitic phase shift which varies as a
function of the .DELTA.t.sub.k of the form:
which conveys the Doppler phase history as a function of azimuthal
time t affecting a target having an azimuth coordinate t'.
The radar/target outward/return propagation time .tau..sub.c is
dependent on the radial distance of the relevant target. It is a
parabolic function of the azimuthal time coordinate t which is
customarily modelled by means of the Doppler parameters.
Restricting ourselves for the sake of simplicity to a finite
expansion of order 2 it is expressed by the relation: ##EQU30##
.tau..sub.c0 denoting the distancewise time coordinate .tau. of the
relevant target, f.sub.c the central carrier frequency of the
pattern, f.sub.dc the mean Doppler and f.sub.dr the Doppler
slope.
Under these conditions, the variable parasitic phase shift
dop.sub.k() due to the azimuthal impulse response can be written:
##EQU31## which shows that the azimuthal impulse response
introduces, in addition to a distance-dependent variable phase
shift tagged by the value of the term tco, a parasitic phase shift
dependent on the relevant spectral sub-band, of value:
##EQU32##
The presence of parasitic phases for each spectral sub-band
introduces considerable degradations into the quality of the
impulse response. To be convinced of this, it is sufficient to
consider the simple example of a synthetic-band waveform pattern
where N=2 and where there is a phase shift .pi. between the
spectral sub-bands. In this case, instead of getting a weighted
sinc azimuthal impulse response akin to a sum channel diagram of an
array antenna, an azimuthal impulse response with two symmetric
main lobes and strong side lobes is obtained, akin to a difference
channel diagram of a monopulse antenna.
As far as the above expression for the parasitic phase shift is
concerned, the two terms of order 1 in .DELTA.t.sub.k are
predominant. However, only the phase term:
does not depend on the azimuthal time coordinate t and can be
compensated for during the pulse compression processing.
This compensation is especially beneficial in respect of so-called
off-aim or SQUINT configurations in which the azimuthal antenna
beam is not perpendicular to the velocity vector of the radar
carrier (SLAR configuration). This is because the mean Doppler
f.sub.dc is then considerable and it is necessary to introduce
compensation for the phase shift which it gives rise to if it is
desired to guarantee good quality of the impulse response after
pulse compression.
It is noted that we are not concerned with the phase shift
introduced by the mean Doppler in relation to the distance
frequency through the term:
appearing in the expression for the signal after pulse compression
of relation (5). To compensate for this phase shift, it is possible
to modify the expression for the transfer function of the matched
filter, adopting the following value for the spectrum of an
celementary pulse of rank k:
instead of:
where .function..sub.dc is a Doppler parameter of order 1 which
may, although not necessarily, be equal to the mean Doppler
f.sub.dc used in SAR radar imaging processing.
With this new phase correction, the following value is adopted for
the expression for the transfer function of the matched filter:
##EQU33##
After matched filtering and distancewise inverse Fourier transform,
the following signal is finally obtained: ##EQU34##
FIG. 3 illustrates the main stages of the pulse compression
processing just proposed.
The raw video reception signal v.sub.0 is available at the output
of the analog/digital converter of the receiver of the radar, in
the form of a table of complex samples with three dimensions: a
dimension k which depends on the rank of the elementary pulse which
is at the origin thereof, in the synthetic-band waveform pattern,
and two time dimensions, one .tau., short-term, which measures the
time which elapses between the transmissions of two elementary
pulses of a synthetic-band waveform pattern, which is
representative of the echo return time and which provides for the
tagging of targets along the distance axis, and the other, t,
longer term, which measures the order of succession of the
transmissions of the synthetic-band waveform patterns, which allows
assessment of the Doppler effect on the echoes of the targets and
which provides for the tagging of targets along a Doppler or
azimuth axis oriented in the direction of movement of the radar
relative to the targets.
The first stage consists in multiplying, with the aid of a bank of
complex multipliers 21, 22, . . . , 23, the samples of the raw
video reception signal v.sub.0,k (.tau., t) of like rank k by a
frequency transposition term:
.DELTA.f.sub.p(k) being the gap of the carrier frequency-of the kth
pulse with respect to the central carrier frequency f.sub.c of the
synthetic-band waveform pattern, given that the elementary pulses
are not in natural order but permuted so as to improve the
effectiveness of the bandpass reception filter, and .tau..sub.0
being the lag after transmission of an elementary pulse, whereafter
consideration of the receipt signal begins.
The second stage consists in carrying out, at 31, 32, . . . , 33,
distancewise spectral analyses, of oversamplings, in a ratio N, of
the raw video reception signals of the various ranks k after their
frequency translations. It makes it possible to obtain the signals
V.sub.1,k (F, t).
The third stage consists in selecting, at 41, 42, . . . , 43 a
useful span in each of the frequency spectra resulting from the
previous spectral analyses, each useful span having a bandwidth B
corresponding to that of an elementary pulse of the synthetic-band
waveform pattern and the various spans, N in number, being shifted
in relation to one another in accordance with the carrier
frequencies of the elementary pulses of rank k to which the
analysed signals correspond, so as to cover a global band
N.times.B.
The fourth stage 51 consists in reconstructing the synthetic band
by juxtaposing the various spans selected in the spectral analyses,
and in performing the pulse compression by matched filtering in the
distancewise frequency domain to obtain a signal V.sub.2 (F,
t).
The fifth and last stage 61 consists of a distancewise inverse
spectral analysis making it possible to go back to the distancewise
time domain and to obtain a raw video reception signal v.sub.2
(.tau., t) with two time dimensions, distancewise and
azimuthal.
FIG. 4 details a first way of carrying out a distancewise spectral
analysis of a signal oversampled in a ratio N, usable in the course
of the second stage of the pulse compression process illustrated in
the previous figure. This first way consists:
in the course of a first stage 300, in oversampling, by a factor N,
the signal before spectral analysis by adding (N-1) null samples
between each starting sample, then
in the course of a second stage 301, in performing the spectral
analysis on the oversampled signal, for example, by a Fourier
transformation or by a high-resolution method.
FIG. 5 details a second way of carrying out a distancewise spectral
analysis of a signal oversampled in a ratio N, usable in the course
of the second stage of the pulse compression process illustrated in
FIG. 3. This second way consists:
in the course of a first stage 310, in performing the spectral
analysis on the starting signal, for example, by a Fourier
transformation or by a high-resolution method, then
in the course of a second stage 311, in duplicating N times the
frequency spectrum obtained.
This second way of operating has a certain advantage over the first
since it makes it possible to reduce the amount of computation
required for the analyses of spectra which are carried out on a
lesser number of samples.
FIG. 6 details a first way of carrying out the reconstruction of
the synthetic band and the pulse compression, usable in the course
of the fourth stage of the pulse compression process illustrated in
FIG. 3. This first way consists:
in the course of a first stage, in carrying out a matched filtering
with regard to each spectral component V.sub.1,k corresponding to
the raw video reception signals in return for an elementary pulse
of rank k, by multiplying with the aid of a bank of multipliers
511, 512, . . . , 513, this spectral component V.sub.1,k by the
conjugate H.sub.i,k of the frequency spectrum of the elementary
pulse of rank k:
with:
where P(F) is the spectrum of an elementary pulse transmitted at
the central carrier frequency of the synthetic-band waveform
pattern and .DELTA.f.sub.p(k) the gap in the carrier frequency of
the kth pulse with respect to the central carrier frequency of the
pattern f.sub.c, or, as a variant, to compensate for a phase shift
introduced by the mean Doppler with regard to the distance
frequency, with:
then,
in the course of a second stage, in reconstructing the global
spectrum of the synthetic band by juxtaposing, by means of an adder
514, the frequency spectra of the various raw video reception
signals which originate from the responses of the targets to the
set of elementary pulses of the synthetic-band waveform pattern
which was transmitted and which have been pulse-compressed.
FIG. 7 details a second way of carrying out the reconstruction of
the synthetic band and the pulse compression, usable in the course
of the fourth stage of the pulse compression process illustrated in
FIG. 3. This second way consists:
in the course of a first stage, in reconstructing the global
spectrum of the synthetic band by juxtaposing, by means of an adder
520, the frequency spectra of the various raw video reception
signals which originate from the responses of the targets to the
set of elementary pulses of the pattern of the synthetic-band
waveform transmitted, then
in the course of a second stage, in carrying out a matched
filtering with regard to the global spectral component obtained
V.sub.1 corresponding to the raw video reception signals in return
for the set of elementary pulses of a synthetic-band waveform
pattern, by multiplying with the aid of a multiplier 521, this
global spectral component V.sub.1 by the conjugate H.sub.i of the
reconstructed global frequency spectrum of a synthetic-band
waveform pattern: ##EQU35## where P(F) is the spectrum of an
elementary pulse transmitted at the central carrier frequency of
the synthetic-band waveform pattern and .DELTA.f.sub.p(k) the gap
in the carrier frequency of the kth pulse with respect to the
central carrier frequency of the pattern f.sub.c or, as a variant,
to compensate for a phase shift introduced by the mean Doppler with
regard to the distance frequency, with: ##EQU36##
The two above-described ways of operating for carrying out the
reconstruction of the synthetic band and the pulse compression are
equivalent by reason of the distributivity of addition, which
allows reconstruction of the global synthetic band, with respect to
multiplication, which allows matched filtering.
After the pulse compression by synthetic band, the raw video
reception signal of a radar can be used for various purposes and in
particular for SAR radar imaging processing but it is then
necessary to take into account a parasitic phase-shift term
introduced by the pulse compression by synthetic band.
This is because, we have seen (relation 6) that the raw video
reception signal after synthetic band pulse compression v.sub.2
(.tau., t) had the expression: ##EQU37##
The first stage of the Doppler part proper of SAR processing
consists in taking the Fourier transform of the compressed signal
along the distance axis. This actually makes it possible to convert
the delay due to the propagation time for each target into a phase
shift related to the Doppler parameters.
In the particular case of the synthetic-band waveform, this
distancewise Fourier transform also gives access explicitly to the
distancewise spectral sub-bands for which the azimuthal impulse
response is different. We thus have: ##EQU38##
The second stage of the Doppler part of SAR radar imaging
processing consists in taking the azimuthal Fourier transform of
the above signal so as to bring out, on the one hand, the Fourier
transform of the desired backscattering coefficient and, on the
other hand, the transfer function of the azimuthal radar imaging
system. On this occasion, the dependence of this transfer function
with regard to the relevant distancewise spectral sub-band will be
clearly revealed in the form of an easily compensatable phase term.
It then follows that: ##EQU39## where H.sub.az denotes the
azimuthal transfer function of the radar imaging system such that:
##EQU40##
By using the modelling of the target outward/return time
.tau..sub.c with the aid of the Doppler parameters, this transfer
function can also be written: ##EQU41##
Going back to relation (7), the presence of a parasitic phase term
is observed:
which is due to the pulse compression of a synthetic-band waveform
and which depends on the spectral sub-band associated with the
elementary pulse of rank k.
To compensate for this parasitic phase term, it is proposed to add
a corrector phase term: ##EQU42## to the expression for the
azimuthally matched filter adopted for a conventional waveform.
It is recalled that the expression for the azimuthally matched
filter for an SAR radar imaging processing is given, to a first
approximation, by:
an effective weighting window often being introduced so as to limit
the level of the side lobes of the azimuthal impulse response,
having the expression: ##EQU43## where W(F) is the useful weighting
window and G.sub.proc an optional factor for compensating for the
gain afforded by the processing such that: ##EQU44## F.sub.r being
the frequency of repetition of the synthetic-band waveform
pattern.
Thus, with the conventional waveform, a relation of the form:
##EQU45## is generally adopted for the expression for the matched
filter.
With the synthetic-band waveform, a matched filter expression of
the form: ##EQU46## will be adopted so as to take account of the
parasitic phase term introduced by the synthetic-band pulse
compression.
After matched filtering and return to the distancewise and
azimuthal time domains by azimuthal inverse Fourier transform
followed by distancewise inverse Fourier transform, the following
signal is obtained:
the product of a convolution of the impulse response after
processing, consisting of the product of two independent weighted
sincs, times the complex backscattering signal from the targets,
translated distancewise so as to take account of the storage of the
digital samples of the raw video reception signal in an analysis
window commencing at the instant .tau..sub.0.
FIG. 8 illustrates the stages of an SAR radar imaging processing
after pulse compression by synthetic band.
The first stage 61 consists in performing a Fourier transform along
the distance axis on the table v.sub.2 (.tau., t) of the samples of
the signal received, which arises from the pulse compression
processing by synthetic band, illustrated in FIG. 3. This operation
makes it possible to retrieve a table of samples V.sub.2 (F, t)
with distancewise frequency variable F. Although it seems to be a
repetition of the distancewise spectral analysis carried out on the
occasion of the pulse compression processing, it has its use since
it allows a prior segmenting into restricted spans of the distance
axis so as to take account of the non-stationarity of the Doppler
effect along this axis. This segmentation leads to repeating the
operations on the various segments of the table of samples with
simpler distancewise Fourier transforms since they pertain to a
lesser number of points. The outcome in terms of the amount of
computation is often favourable.
The second stage consists in performing an azimuthal Fourier
transform 62 so as to retrieve a table of samples V.sub.2 (F,f)
with both distancewise and azimuthal frequency variables.
The third stage consists in carrying out the matched filtering by
multiplying, in a complex multiplier 63, the samples of the table
V.sub.2 (F,f) by the transfer function: ##EQU47## taking into
account a phase compensation pertaining to the prior pulse
compression processing by synthetic band, with a different value
depending on the relevant distance spectral regions.
The fourth stage consists in performing an azimuthal inverse
Fourier transform 64 so as to go back to the azimuthal time
domain.
The fifth and last stage consists in performing. a distancewise
inverse Fourier transform 65 so as likewise to go back to the
distancewise time domain and obtain a table v.sub.3 (.tau., t) of
the samples of the backscattering signals of the targets making it
possible to plot an image in two dimensions along the distance and
azimuth axes.
* * * * *